When taking a photo with a common camera, if the focus is on an object, different degrees of out-of-focus phenomenon may occur in areas that are not at the same depth as the object. According to the thin-lens imaging system model, the degree of out-of-focus is proportional to the depth of the scene. The farther the object is from the focal plane, the greater the blurring degree is. Photographers deliberately take out-of-focus blurred photos to achieve artistic effects, but blurred images lose many details, and sometimes we need to avoid out-of-focus blurring, so debluring processing of a single image is significant.
The degradation (decrease in image quality) model of out-of-focus images can be expressed as the following convolution process:I=L⊗k+N,  (1)where I and L denote an out-of-focus blurred image and a clear image, respectively, ⊗ is the convolutional symbol, N is random noise, and k is a blur kernel. In out-of-focus blurring, the blur kernel is often considered as a Gaussian model:
                                          k            ⁢                                                  ⁢                          (                              x                ,                y                ,                σ                            )                                =                                    1                                                                    2                    ⁢                    π                                                  ⁢                σ                                      ⁢                          e                              -                                                                            x                      2                                        +                                          y                      2                                                                            2                    ⁢                                          σ                      2                                                                                                          ,                            (        2        )            where (x,y) are the coordinates of a pixel in the image, a is the standard deviation, which can measure the blur degree of the image, also known as the blur amount.
The blur kernel estimation is a key step in deblurring processing. For spatially consistent images, since the blur kernels are the same at various locations on the image, deblurring the image in this case is simpler. For spatially variable blurred images, each pixel in the image has a different blur kernel, which is more complicated and deblurring the image is more difficult. At present, there are mainly two methods to estimate the blur kernels of a single spatially variable blurred image: in the first method, the image is divided into rectangular areas of equal size according to the similarities of blur kernels. Spatial sparse constraints are used to constrain the blur kernel in each area to obtain the local blur kernel k of the image. The other method considers the blur kernel as a disc model or a Gaussian model, and estimates the radius of the disc corresponding to each pixel or the standard deviation of the Gaussian model to obtain blur kernels. Since the blur degree in the local area of the image is depth dependent, dividing the image into rectangular areas of equal size easily causes great difference between the actual blur degree of different pixels in the same rectangular area, so the local blur kernel estimation is not accurate in the first method. A corresponding blur kernel for each pixel is obtained in the second method, but it spends too much to deconvolute each pixel by using different blur kernels respectively during image restoration. Therefore, how to use these blur kernels for image restoration is a key issue.
At present, it is proposed to divide the blur amounts a into different orders of magnitude, and take the minimum value of each order as the value of the blur amounts at this order. Ringing artifacts are eliminated in this method (The Ringing artifact is one of the factors that affects the quality of restored image due to using improper model in image restoration. The direct cause of the ringing artifacts is loss of information in the image degradation process, especially the loss of high-frequency information, which seriously degrades the quality of the restored image and it is difficult to carry out subsequent processing of the restored image). However, since the final estimated blur amount is less than the actual one, the restored images are still relatively blurring.
In summary, as a key step in image processing, deblurring a single spatial variable out-of-focus image has drawn much attention and a large number of deblurring algorithms have emerged. However, there are still many problems with the blur kernel estimation and the final image restoration, which requires further improvement.